Multiple-distribution Regularized Lattice Boltzmann Method For Convection-Diffusion-System-Based Incompressible Navier-Stokes Equations

In this paper, a multiple-distribution regularized lattice Boltzmann model for solving the incompressible Navier-Stokes equations is proposed. The core idea of the model is to convert the incompressible Navier-Stokes equations into a coupled convection-diffusion system, for which the regularized lattice Boltzmann method is modeled. Then, the Chapman-Enskog analysis proves that the model can accurately recover the incompressible Navier-Stokes equations based on the convection-diffusion system. In addition, we derive the formulas for the direct calculation of velocity and pressure by using the zeroth-order moment and first-order moment of the distribution function, and the first-order moment of the non-equilibrium distribution function for the local calculation of velocity gradient, velocity divergence, strain rate tensor, shear stress, and vorticity. Finally, we verify the validity and accuracy of the present model through a series of benchmark solution examples as two-dimensional poiseuille flow, simplified two-dimensional four-roll mill problem, and two-dimensional lid-driven cavity flow, and through numerical tests, we found that the model has a second-order convergence rate spatially. At the same time, compared with the MDF-MRTLB model, the MDF-RLB model has higher computational efficiency, and the computational time is reduced by more than 7%.